0.1 Introduction & Summary

An accurate home price prediction algorithm can reduce volatility in the housing market and take into account existing factors that may not be reflected in a home’s previous selling prices (e.g., new roof, new shopping center, etc.) However, predictive algorithms can also be exceedingly difficult to perfect. A falsely high average estimate in a neighborhood might lead home sellers to list their homes at too high an asking price and dragging out the process of selling their home, thereby introducing friction into the housing market. A falsely low estimate may depress the value of what is oftentimes a homeowner’s most valuable asset.

This project attempts to predict housing prices in metropolitan Miami by taking into consideration a home’s unique features (e.g., fence, patio) as well as considering local amenities and external features like schools, parks, and access to major roads. One interesting finding from this process is that a home’s location in a middle school zone shows a positive relationship with home prices, but bot elementary or high school zone.

To create our model, we converted our features of interest into variables that can be fed into an OLS regression model. We tested each featured for correlation with home sale prices and fine-tuned our model until we were able to minimize error.

After testing and rejecting several features that did not deduce our prediction errors (e.g., distances to nearest park, major road, and middle school), we ultimately settled on the features (dependent variables) listed below.

  1. Location/External Features
    • Property.City: Miami, Miami City
    • GEOID: Census tract code
    • Shore1: distance from shoreline (feet)
    • MedRent: median average rent by census tract
    • pctWhite: % residents who identify as White
    • pctPoverty: % residents below poverty line
    • 9 binary variables for middle school area: Brownsville, Citrus Grove, Jose de Diego, Georgia Jones-Ayer, Kinloch Park, Madison, Nautilus, Shenandoah, West Miami
  2. Internal Features
    • LotSize: lot square footage
    • Age: years since home was built
    • Bed: number of bedrooms
    • Bath: number of bathrooms
    • Stories: number of bathrooms
    • Pool: extra pool feature (0/1)
    • Fence: extra fence feature (0/1)
    • Patio: extra patio feature (0/1)

0.2 Data

Summary Statistics
Statistic N Mean St. Dev. Min Max
SalePrice 2,066 405,476.400 199,741.700 12,500 1,000,000
LotSize 2,066 6,360.875 1,721.617 1,250 17,620
Age 2,066 70.954 18.186 -1 115
Stories 2,066 1.073 0.265 0 3
Bed 2,066 2.692 0.794 0 8
Bath 2,066 1.611 0.700 0 6
Pool 2,066 0.108 0.310 0 1
Fence 2,066 0.738 0.440 0 1
Patio 2,066 0.499 0.500 0 1
Shore1 2,066 7,047.549 5,248.614 88.597 26,528.540
MedRent 2,040 1,042.535 311.133 246.000 2,297.000
pctWhite 2,062 0.703 0.320 0.057 0.989
pctPoverty 2,062 0.217 0.108 0.052 0.556
Brownsville.MS 1,588 0.098 0.298 0.000 1.000
CitrusGrove.MS 1,588 0.115 0.319 0.000 1.000
JosedeDiego.MS 1,588 0.129 0.335 0.000 1.000
GeorgiaJA.MS 1,588 0.133 0.340 0.000 1.000
KinlochPk.MS 1,588 0.196 0.397 0.000 1.000
Madison.MS 1,588 0.001 0.035 0.000 1.000
Nautilus.MS 1,588 0.061 0.240 0.000 1.000
Shenandoah.MS 1,588 0.243 0.429 0.000 1.000
WestMiami.MS 1,588 0.024 0.153 0.000 1.000

0.3 Method

Training Set LM Results
Dependent variable:
SalePrice
(1) (2)
Folio 0.00000
(0.00000)
Property.CityMiami Beach 220,589.400**
(102,729.500)
LotSize 17.974***
(1.660)
Bed 8,653.610*
(4,483.327)
Bath 4,613.343
(5,440.150)
Stories 13,854.920
(11,214.380)
Pool 77,281.650***
(9,820.892)
Fence -149.050
(5,646.349)
Patio 4,073.120
(5,115.939)
ActualSqFt 67.033***
(6.231)
Age -698.975***
(147.148)
Shore1 -5.745*** -3.369***
(1.229) (1.030)
MedHHInc 1.370*** 1.091***
(0.234) (0.193)
TotalPop 4.453** 3.400**
(1.797) (1.481)
MedRent 8.011 10.111
(16.927) (13.970)
pctWhite 87,738.750*** 72,584.590***
(21,213.910) (18,038.400)
pctPoverty -65,160.580 -28,329.320
(46,955.060) (38,669.420)
Brownsville.MS -74,321.900** -19,595.140
(35,665.230) (29,848.970)
CitrusGrove.MS -63,085.380* -16,536.970
(33,757.230) (27,908.010)
JosedeDiego.MS -24,574.030 41,689.690
(36,087.170) (30,171.430)
GeorgiaJA.MS -83,659.540** -21,745.790
(33,968.440) (28,569.970)
KinlochPk.MS -20,898.120 7,151.547
(23,871.550) (19,733.870)
Madison.MS -102,752.000 -24,901.940
(89,066.670) (73,254.900)
Nautilus.MS 229,234.000***
(37,774.810)
Shenandoah.MS 99,482.560*** 122,292.100***
(31,097.140) (25,991.120)
WestMiami.MS
Constant 274,559.400*** -5,246.435
(50,967.110) (142,697.300)
Observations 1,584 1,584
R2 0.603 0.736
Adjusted R2 0.599 0.732
Residual Std. Error 113,746.600 (df = 1569) 93,070.580 (df = 1559)
F Statistic 170.158*** (df = 14; 1569) 180.949*** (df = 24; 1559)
Note: p<0.1; p<0.05; p<0.01

#our best model was reg.cv2

0.4 Results

The first regression we combined our feature engineering variables to see which were statistically significant. The second regression includes all of the off-the-shelf features with our custom features. Model improves a lot by R2.

0.4.1 Commented out some plots b/c don’t think they’re needed (See Below)

intercept RMSE Rsquared MAE RMSESD RsquaredSD MAESD
TRUE 130147.8 0.7933946 93060.55 354594.9 0.2778949 210570.7
intercept RMSE Rsquared MAE RMSESD RsquaredSD MAESD
TRUE 98912.42 0.709759 82492.1 52113.41 0.271611 39852.27